Spurs boss Mauricio Pochettino is believed to be a fan of the youngster.
Tierney has a value of £20 million according to the Mirror which put Spurs off from making a bid during the recent transfer window.
However, Spurs might try to purchase the player at a bargain price in January because of Celtic’s elimination from this season’s Champions League.
Brendan Rodgers’ troops were dumped out of Europe’s Premier Club competition before the group stages after losing their third qualifying round tie 2-1 to AEK Athens last week.
The Scottish giants may need to sell Tierney in order to make up for the financial loss that they will suffer because of their elimination.
With Danny Rose being strongly linked with an exit from Spurs, Tierney could prove to be a good replacement.
Despite having turned 21 only two months ago, Tierney has already served as captain for both Celtic and the Scottish national team at senior level.
He has a bright future of him and he should look to play in one of the top European Leagues in the near-future.
Tierney also fits the profile of a player that could succeed under the guidance of Pochettino.